To determine the correct inverse operation to verify the equation [tex]\(102 \div 3 = 34\)[/tex], we need to find which operation, when applied, reverts back to the original value or confirms the given division statement.
Let's analyze each option:
Option A: [tex]\(102 \div 34 = 3\)[/tex]
This checks if dividing 102 by the result, 34, yields the original divisor, 3. This method re-evaluates the relationship but does not directly verify the division in reverse.
Option B: [tex]\(34 - 3 = 31\)[/tex]
This operation performs subtraction, which is unrelated to verifying a division operation. Since it does not involve the original dividend (102), it cannot be used for verification.
Option C: [tex]\(3 + 34 = 37\)[/tex]
This adds the divisor and the quotient, giving a sum unrelated to the values we are concerned with in verifying the original division.
Option D: [tex]\(34 \times 3 = 102\)[/tex]
This multiplies the quotient (34) by the divisor (3) to see if we arrive at the original dividend (102). This operation directly verifies the original division by reversing the operation.
Thus, the inverse operation that correctly verifies the given equation [tex]\(102 \div 3 = 34\)[/tex] is:
[tex]\[ \boxed{34 \times 3 = 102} \][/tex]
Therefore, the best answer is:
[tex]\[ \text{D. } 34 \times 3 = 102 \][/tex]
